Apparatus and method for automatic splitting of die cavities

ABSTRACT

Apparatus and method for automatically splitting a die cavity including means for storing signals representative of significant characteristics of the contour of the die cavity and means responsive to the storing means for processing the stored signals to determine split lines for dividing said cavity into segments which can be expeditiously machined.

United States Patent McFadden et al.

[ June 17, 1975 1 1 APPARATUS AND METHOD FOR AUTOMATIC SPLITTING OF DIE CAVITIES [75] Inventors: Daniel G. McFadden, Parsippany;

Richard C. Levine, Plainfield, both of NJ.

[73] Assignee: DieComp, Inc., South Plainfield,

[22] Filed: Sept. 29, 1972 [21] App1.N0.: 293,314

[52] U.S. Cl. 235/l5l.l; 76/4; 76/107 A; 164/6 [51] Int. Cl..... 822d 45/00; 006g 7/48; G061 15/20 [58] FieldofSearch ..235/l51.l,151.151.11,

235/150; 444/1; 29/527.6, 529, DIG. 10; 76/4, 107 R, 107 A, DIG. 3; 83/71, 32, 54, 55;164/1, 4, 6,10,17,18, 23, 24,174; 72/7-9 360, 362

[56] References Cited UNITED STATES PATENTS 12465511 4/1966 Galley ct :11 BBS/151.1 UX 1490,3120 1/1970 Valembois et ul. 83/71 X 3.596.068 7/1971 Doyle 235/151 X 3.605.528 9/1971 Whitacre et a1, v. 76/107 Primary Examiner-Joseph F. Ruggiero Auorney, Agent, or Firm-Joseph .1. Baker; Gerald J. Ferguson, Jr.

[57] ABSTRACT Apparatus and method for automatically splitting a die cavity including means for storing signals representative of significant characteristics of the contour of the die cavity and means responsive to the storing means for processing the stored signals to determine split lines for dividing said cavity into segments which can be expeditiously machined.

34 Claims, 12 Drawing Figures PATENTEDJUN 17 1915 FIG. I

CELLS CONTAINING CO-ORDINATES OF SIGNIFICANT POINTS OF THE CONTOUR [TEMPORARY STORAGE ems FIG. 2A

CELLS CONTAINING SYMMETRY AXIS DIRECTIONS CELLS CONTAINING CENTER CO-ORDINATES SWITCHING AND CONTROLLING MEANS PROCESS I PROCESS 2 PROCESS n OUTPUT SIGNAL CHANNEL INACCESSIBLE FIG. 2B

CONTOUR FOR SPLIT IT PATENTEDJUN I T I975 5.889.876 SREET 3 SOURCE OF SOURCE OF TRIGONOMETRIG LENGTH SOuRcE OF 320 OuANTITY QUANTITY 32b SIGNAL REPRESENTING INOEx NUMBER OF THE OuRRENT IO 33 33 x 3 SPLIT wEIGIITEO O 3T E 33 IVSUM SIGNAL 1 GATE SOURCE OF -37 SYNC PULSE COMPARATOR {TRIGGER GATE PULSE TEMPORARY CELL TEMPORARY CELL FIG, 4 STORING PREVIOUS STORING INDEX NUM.

MAxIMuM WEIGHTED 0F PREvIOuS MAXIMUM SuM SCORE vALuE L SCORE SPLIT L SPLIT X2 ANGLE 3122 x SIGNAL I 45 4O OIvIOER GOINOIOENOE 0 lb ARCTAN GATE 1 TRIGGER ROOTER 43 44 FIG. 5 s

TRANSMISSION AOOuMuLATOR GATE GELL PATENTEDJUII I 7 I975 .889876 S'riEU 6 FIG. I0

I26 H I x cIRcuITRY FOR I32 Y DETERMINING C HORIZONTAL CO-ORDINATE IN ROTATED SYSTEM YB I36 52 OR C I x cIRcuITRY FOR I34 DETERMINING x VERTICAL CO-ORDINATE IN ROTATED SYSTEM YB I" sIN cos sINE cosINE I Z I I x i I l i I30 C if: $EZT-F- mgg g gg VERTICAL C0-ORDINATE AMPLIFIER IN ROTATED SYSTEM APPARATUS AND METHOD FOR AUTOMATIC SPLITTING OF DIE CAVITIES CROSS-REFERENCES TO RELATED APPLICATIONS This application is related to copending US. application Scr. No. 66,533 filed Aug. 24. 1970 by Richard C. Levine and entitled Automatic Method and Appara tus for Fabricating Progressive Dies; copending US. application Ser. No. 284,879 filed Aug. 30. I972 by Daniel G. McFadden and Richard C. Levine and entitled Method and Apparatus for Automatic Optimal Layout of Shapes to be Cut from Material"; and copending US. application Ser. No. 287,262 filed Sept. 8, I972, now US. Pat. No. 3.8l8,l95 by Richard C. Levine and entitled Apparatus and Method for Controlling Placement of Split Die Cavities", all of the foregoing applications being incorporated herein by reference.

BACKGROUND OF THE INVENTION 1. Field of the Invention This invention relates to die design and, in particular, to automatic splitting of die cavities.

2. Description of the Prior Art In the past, the total design of dies for the stamping of sheet metal has been accomplished by skilled and experienced human designers. In recent years. aspects of the techniques of design of dies have been accomplished by mechanical and electronic means such as those described in the heretofore mentioned copending applications.

One portion of the design process consists of splitting" the die cavities so that the cavity in the die is surrounded by two or more pieces of metal (or carbide composition material) which form portions of the cavitys cutting edges. The split must be located so that each of the two (or more) pieces of metal (die segments) which surround the cavity can be machined practically and economically by a grinding wheel. In addition, the shape of the resultant die segments should be strong, free of weak projections and acute angles.

Until the present invention, the design of the die and in particular the location and directions of the cavity splits were carried out by a human die designer, on the basis of his knowledge and experience. Different practices of die design followed by different designers produced differing results when several human designers were assigned the project of designing a die for manufacturing the same part. Aside from the non-uniform results of human designers, the increased use of numerical control machining requires a Cartesian co-ordinate description of the components of the die. The human designer works with pictorial representations in the form of mechanical drawings made by pencil on paper. Heretofore, to produce geometrical co-ordinate descriptions of each individual object in a die design, a second skilled technician, known as a part programmer", has examined the finished drawing and laboriously copied the geometrical data, point by point, so that a NIC tape could be prepared for controlling a numerically controlled machine tool.

SUMMARY OF THE INVENTION One object of this invention is to provide a rapid, automatic, and consistent splitting design for die cavities which may be part ofa process of automatic die design.

Another object of this design is to process signals which represent the geometric co-ordinates of the cavities which must be produced, and thus develop output signals which are compatible with various numerically controlled machine tools and also with various machines which produce drawings on paper by moving a pen under control of the geometric co-ordinate signals.

Another object of the invention is to produce a die design more quickly than it could be produced by a human designer.

Other objects and advantages of this invention will become apparent upon reading the appended claims in conjunction with the following detailed description and the attached drawing.

BRIEF DESCRIPTION OF THE DRAWING FIG. I is a block diagram of an illustrative overall system configuration of this invention.

FIGS. 2A, 2B. and FIG. 3 are outlines of cavity configurations illustrating certain features of this invention.

FIG. 4 is a block diagram of illustrative circuitry for determining a preferred pair of cavity split lines.

FIG. 5 is a block diagram of illustrative circuitry for calculating the total length ofthe sides parallel to a predetermined axis of symmetry of the die cavity.

FIG. 6 is a block diagram of illustrative circuitry for determining if an axis of symmetry intersects a concave portion of the die cavity.

FIG. 7 is a graph illustrating the intersection of an axis of symmetry with a concave die cavity portion.

FIG. 8 is a block diagram of illustrative circuitry for determining the center of force of a configuration.

FIG. 9 is a graph illustrating a configuration and how its center of force is determined.

FIG. 10 is a block diagram of illustrative circuitry for determining the existence of axes of symmetry in a die configuration.

FIG. 11 is a graph illustrating how the circuitry of FIG. 10 determines axes of symmetry.

DESCRIPTION OF THE PREFERRED EMBODIMENTS The method and apparatus of this invention may utilize circuitry which possesses signals representing geometric co-ordinates of the contour which forms the outline of the cavity. The Cartesian or geometric coordinate values can be represented by the amplitude of a physical signal such as the voltage of an electrical waveform. This waveform can be continuous in both time and amplitude, or discontinuous and quantized in either time or amplitude or both. If the signal is quantized in this way, it could also be represented by distinct digital patterns to represent the discrete co-ordinates, each pattern representing a different significant point on the contour. Such numerical signals must be used and reused frequently during the operation of the invention. It is therefore expeditious to store such numerical information in an electrical or magnetic form in a device such as a magnetic disk or magnetic core mem ory system associated with an electronic data processing system. The numerical data can thus be easily accessed as needed by other portions of the invention.

To describe the various means which may be used to store the numerical data describing the geometric coordinates of various significant point on the outline of the contour, this specification will use the generic term "cell" which may represent any one of the means described above, or other means of making numerical data accessible to the remainder of the system. Data describing the geometric co-ordinates of a point is obtained from a cell or cells as appropriate.

The general structure of the invention is described in FIG. I. A bank of cells contain the numerical values of significant points on the contour. These values may be manually keyed through an appropriate keyboard by a part programmer to cells 10. they may be provided by a drawing co-ordinate digitizing machine of the type described in copending application Ser. No. 66,533. or the die contour may be continuously scanned and quantized samples taken each time the slope changes. Thus, the cells 10 would contain, for example, the coordinates of all the end points where straight lines or arcs meet adjacent sides or arcs in the contour. For clarity and brevity, arcs can be represented by storing the co-ordinates of the center of the arc. the numerical value of the radius in addition to the end points, and a binary value to indicate whether the arc is concave or convex.

A given contour may have various axes of mirror symmetry. For example, a regular hexagon has six distinct axes of mirror symmetry. Some contours, of course, have no symmetry whatever. For those contours which have one or more axes of symmetry, a number representing the angle of each such axis is stored in one of the cells 12. These are available for testing by the remainder of the apparatus.

A test center is used for certain tests, and its coordinates are stored in a cell 13. This point may represent the centroid of the area of the contour, or the centroid of force of the contour, but it is typically some significant internal point used as a test center. Circuitry for deriving the information stored in cells 12 and 13 is described hereinafter.

The routing of signals from the cells to the processors is performed by switching and controlling means 14 which performs a function analogous to a telephone switchboard. In a general purpose computer, this function is accomplished by the memory addressing means and the central processor unit under the direction of a stored program of distinct instruction steps. Various operations performed on the signals taken from cells l0, l2, and 13 are performed by directing the signals to special processors 16 and/or temporary storage cells which are used to store intermediate results.

Several methods will now be described by which this apparatus and method can be used to automatically generate the preferable split line for a die cavity. In a first example, we consider a part which has several axes of symmetry. An axis of symmetry is preferably as a split line if it has a large total length of contour sides parallel to it, and does not cut a concave are on the contour. In addition, other factors being equal, the split which is closer to vertical is preferable in certain types of die construction.

The reason for rejecting a split which intersects a concave side is that the resulting segments will contain a hidden" portion which will not be accessible to a grinding wheel. An example is given in FIG. 2A. The contour shown has two symmetry axes I7 and 18. Axis 17 would not be suitable because it intersects concave arcs at the top and bottom producing contours which are inaccessible for grinding. Therefore. axis 18, which does not have this deficiency, is the preferable axis for splitting.

Another example, in FIG. 2B, shows a hexagon with its six symmetry axes labeled I9 through 24. In this example axis 24 is preferable for two reasons. First, it. together with axes 20 and 22, has many long sides of the hexagonal contour parallel to it. In addition to this, it is the closest to vertical of any of these axes and is thus preferable overall.

The sequence of operations in the invention for processing a contour with mirror symmetry axes is as follows. The switching means 14 scans the cells l2, describing the symmetry axis angles in a well known manner which may be under stored program control. For each axis the signals are directed to the appropriate processors, which test for the intersection of that particular axis with any concave arc in the contour. This takes place by means of scanning the cells 10 which describe the various sides of the contour, which will be described in detail hereinafter. It this is not cause for rejection, the second step is to determine the total length of all lines in the contour which are parallel to the given axis. In addition, the absolute magnitude of the trigonometric sine of the axis angle is a quantitative measure of how close to vertical the particular axis is where the vertical axis is at An efficacious method used in this invention for determining the preferable axis when two factors both enter into the evaluation of the relative preference is to combine the two numerical factors in a weighted sum. The numerical result can be compared with the corresponding result for an alternate axis for a determination of which is preferable. The weighting factors used in this evaluation are chosen to reflect the relative importance of the two factors involved in the decision process of which split axis is preferable.

For example, in FIG. 2B, consider the case where the sides of the hexagon are each 20 millimeters long. If the relative factors for the absolute sine of the split angle and the cumulative parallel side length are 10 and 3 respectively, then we can compute the score for axes 22, 23, and 24. They are respectively, as follows:

for Axis 22: l0 .5 3X40 for Axis 23: l0 .866 3X0 8.66

for Axis 24: lOXl. 3X40 It is apparent from these numbers that axis 23 is much less preferable than the other two, and that axis 24 is preferable to axis 22.

A second procedure occurs when there is either no axis of symmetry whatever, or such axes of mirror symmetry as do exist are all rejected due to intersections with concave sides of the contour. In such cases, the cells 10 containing the geometric description of the significant points on the contour are scanned to determine a pair of points which are suitable for a split in the cavity, as will be described in detail hereinafter.

As an example, consider the contour in FIG. 3. It has no axis of symmetry. Possible splits may originate from all convex arcs or straight line sides. Thus a set of possible split points are marked and labeled with the numbers 25 through 32. The system can scan all pairs of points (when two splits are desired) and determine the preferable pair.

In this case, two criteria may be used to establish the weighted sum score for each pair. One criterion is the absolute distance between the two points, since we wish to split the cavity at points which are close to diametrically opposite each other. Another feature is the possibility of having the two splits parallel to each other since this is desirable from a fabrication point of view. Parallel lines in the shape of the die segment reduce the total number of grinding tool setups and make the fabrication of the die faster and less expensive. Further. in some instances, it is possible and preferable to shift one of two parallel splits so that they are co-linear.

Since the splitting is usually made so that the split line is perpendicular to the contour, the angle between two split lines is determined by finding the angle between the two sides that the split contacts. The tangent line to an are at the split point is used rather than the arc itself in this case. The magnitude on the trigonometric cosine of the angle between two such sides is a quantitative measure of their closeness to parallelism. since the value of the cosine will be one when they are parallel and zero when they are perpendicular.

In the example of FIG. 3, which is not to scale, there are a total of eight points and these can compose a total of 28 distinct pairs. In general, for n points, there are n'(n-1)/2 distinct pairs. A weighted sum is formed for each point pair, weighing the trigonometric cosine by a factor of IO and the vertical distance by a factor of 3 as in the previous example, the weighting factor, of course. being illustrative. Then the scores for various representative point pairs are as follows:

From the above results, the split at points 27 and 30 as indicated on FIG. 3 is the preferable split over using points 26 and 30 by a slight margin. It is far preferable to any of the other pairs shown above.

It should be apparent to one skilled in the die construction art that the criteria included in the above examples, namely verticality, lack of intersection with a concave side, cumulative parallel side length, mutual distance, and parallelism, are only representative of many criteria which may or may not be significant in a particular type of die construction. In some cases, a horizontal split of a symmetric cavity may be preferable to a vertical one due to the type of die holder being used. In such a case, the trigonometric cosine would be used in place of the sine in the appropriate weighted sum. In other cases the relative importance of parallelism in the two split lines may be of greater significance to a die maker in terms of machining time and the weighting factor of 10 might be increased.

In addition, other features including, but not limited to, the following might be of importance to a particular die design. Such features might include the portion of one side which overlaps the other in a perpendicular projection, or the magnitude of the difference between the area subdivided by a line between the point pair under test and 50% of the total area, or other features. Numeric values could also be assigned these features reflecting their weighted contribution of the total score of these features.

In addition, the extension of the use of this invention to the case of triples of points to include those cavities which are most expeditiously split by three lines should be obvious to one skilled in the electronics and the die design arts from examination of the disclosure. In general. for n points, there are ntn-l )(n-2)/6 distinct triples.

As a representative processor used in the determination of the optimum split for both symmetrical and nonsymmetrical cavities, FIG. 4 is a block diagram of illustrative circuitry which compares and stores both the current best score during a scan of a set of split axes. and also the index of the axis having that best score. At each step of the scan, the new signals from source 32a and 32b representing the trigonometric sine of the angle and the cumulative length parallel to the split are sent to this structure (in the case of a symmetrical cav ity), where they are multiplied by appropriate weighting factors ten and three by means of the two multipliers 33 and the respective products are added in the summer 34.

Each step of the scan, a synchronizing pulse from source 34a causes the comparator 35 to compare the current score with the best previous value stored in the temporary cell 36. If the current value exceeds the best previous value, the comparator outputs a trigger pulse to two gate circuits 37. When triggered, these circuits pass the current score and index number (from source 37a) to the two temporary storage cells 36 and 38 respectively, whereupon they overwrite the previous values and take their place. At the end of a complete scan of all the splits, cell 28 will contain the index number of the preferable split. The switching and control means 14 of FIG. 1 can then utilize this value to direct the direction of the preferable split to the output.

The directions of the splits are stored as angles in cells 12. It is well known to those skilled in the art that the signal representing the angle can be directed to the input of a non-linear function generator which will produce as output the corresponding trigonometric sine to any desired degree of accuracy. Thus, the source 320 is not shown in more detail.

The determination of the cumulative parallel side length is carried out by the apparatus of FIG. 5, this corresponding to the source 32b for symmetrical cavities. For each different angular split, the switching and control means I4 scans the entire set of cells 10 and passes the x and y co-ordinate signals of the end of each straight line side to the circuitry of FIG. 5. The lines labeled X and X represent x co-ordinates of the two ends of the straight line side, Y, and Y represent the corresponding y co-ordinate signals. These signals are applied to summing devices 39 which produce output signals equal to, respectively, the horizontal and vertical projections of the particular straight side being scanned. These signals are applied to a divider 40 which forms their ratio, which itself is fed to a nonlinear function generator 41 which produces a signal equal to the arc tangent of its input, or the angle of the side. If this angle is equal to the angle of the particular split currently being scanned (indicating parallelism), the comparator 42 outputs a trigger pulse. This trigger pulse causes a transmission gate 43 to pass a signal (from circuit 47), equal to the length of the side, to an accumulator cell 44 where it is added to the sum of all similar previously recorded values of length to produce the cumulative parallel side length.

The length signal for this particular side is produced by generating the square of the two projection signals in the multipliers 45 and then adding these in summer 46 to produce a signal which is fed to a square root device 47. another non-linear function generator. the out put of which is the length of the side.

The source 321: for non-symmctrical cavities is readily ascertained from the circuitry of FIG. inasmuch as the angle between the splits at two sides is the angle between the sides (since the splits are perpendicular to the sides or to the tangent to a cum ed portion Thus. using elements the same as elements 39. 40. and 4], the angles of each side may be determined. the difference between the angles is the angle between the splits.

The source 32b for a nonsymmetrical cavity is also readily ascertained from the circuitry of FIG. 5 where the distance between each pair of points on the cavity contour may be determined from elements the same as elements 39, 45, and 47.

As mentioned hereinbefore, a test is made to determine if an axis of symmetry passes through a concave portion of the die. The circuitry for accomplishing this is shown in FIG. 6 and operates as follows. Reference should first be made to FIG. 7. There is an axis of symmetry X,,, which passes through a point X Y, which may be the center of force of the die cavity configuration. which is determined by circuitry which is described in more detail hereinafter. The co-ordinates of the end points of the concave are are specified in FIG. 7 as being X,, Y, and X Y Thus, it can be seen in FIG. 7 that the line of symmetry X under consideration does indeed intersect the concave portion of the die cavity. Thus, in order to determine this a new coordinate system is established. the abscissa of which is coextensive with X,,, the co-ordinate Y,, of which passes through the point X Y,-. The function of the circuitry of FIG. 6 is to determine the y co-ordinates of the concave portion end points in the rotated coordinate system defined by X,, and Y If these latter y co-ordinates are of opposite sign, then the axis of symmetry intersects the concave portion since the axis of symmetry is made coextensive with the rotated abscissa X,,. The general formulas for calculating the y coordinate in the rotated system is as follows: y ==(X,.+X,-) sinoz+(y,,-y -)cosa where x,,. y,, are the coordinates of the point in the original co-ordinate system and X, and Y are the co-ordinates in the original coordinate system of the center of force, which is stored in cell 13 and a is the angle between the co-ordinate systems.

Thus, referring now to FIGS. 5, 6, and 7, the circuitry within the dotted line 50 effects the transformation of the y coordinte y, in accordance with the above formula where the input angle a has the sine and cosine thereof taken at circuits 52 and 54. The difference between X, and X(' is formed at summer 56 while the difference between Y, and Y is formed at summer 58. The difference produced by summer 56 is multiplied by sina at multiplier 60 while the difference produced by summer 58 is multiplied at multiplier 62. The resultant products are then added at summer 64 to produce the y co-ordinate corresponding to Y, in the rotated coordinate system. This signal is then applied to diode 68 while the y co-ordinate corresponding to Y in the rotated co-ordinate system is applied to diode 70, this latter rotated y co-ordinate being determined by circuitry 72 which is the same as circuitry 50. The diode 68 and 70 will permit only positive signals to be applied to exclusive OR circuit 74. The output of exclusive OR circuit 74 is applied to AND circuit 76 together with a sigmi] (from source 7'7. which is responsive to cells 10) which indicates whether the portion of the die under insepction is concave or not. The concavity determination can be readily made by a part programmer as described hereinbefore or by other means for automatically inspecting the contour of a configuration. The concave signal applied over line 78 will be a logical ONE. if the die segment portion is concave and a logical ZERO. if convex. Hence. assuming that the die segment portion is concave and assuming that the axis of symmetry does intersect a concave portion. the rotated co-ordinate corresponding to Y, will be positive as can be seen in FIG. 7 and thus. an output signal will ap pear from diode 68. However. the rotated y co-ordinate corresponding to Y,, will be negative and thus no output signal will appear from diode 70. Hence, the conditions for the exclusive OR circuit 74 are satisfied and a logical ONE signal will appear at the output signal thereof whereby an output signal will also appear from AND circuit 76 thereby indicating that the particular axis of symmetry is unacceptable. If the axis of symmetry did not pass between the end points of a concave die segment portion, then the y co-ordinates in the rotated system would be either both positive or both negative inasmuch as the abscissa of the rotated system is always coextensive with the axis of symmetry, as stated above. Hence, if they are both positive, output signals will appear at both of the diodes 68 and 70 whereby the conditions for exclusive OR circuit 74 are not satisfied. Hence, no output signal will occur from AND circuit 76 whereby the axis of symmetry will be deemed acceptable. If both of the y co-ordinates of the end points are negative, no output signals will appear from either the diodes 68 and 70 and once again, the exclusive OR circuit 74 will not be satisfied, again indicating an acceptable axis of symmetry.

Reference should now be made to FIG. 8 which shows illustrative circuitry for determining the coordinates of the center of force ofa contour. Generally. the co-ordinates of the center of force are given by the following formulas.

: Elihgfh It i715]? i 2 (length of lint: Ia)

" 5 mass (rims where X the x co-ordinate of the center of line it and Y the y co-ordinate of the center of the line k.

Referring to FIG. 9 there is shown a configuration, the end points of one side of which are X,, Y and X Y X and X, are applied to terminals 80 and 82 of FIG. 8 while co-ordinates Y and Y, are applied to terminals 84 and 86. X and X, are added to one another at summer 84 and one-half of this sum is then taken at multiplier 86. This corresponds to the co-ordinate X shown in FIG. 9. The co-ordinate y, is determined in a similar manner by summer 88 and multiplier 90, the multipliers 86 and multiplying the sums from summers 84 and 88 by one-half as indicated in FIG. 8. The distance between the points X,, Y, and X Y are determined in the following manner whereby the difference between X and X, is determined at summer 92,

9 this difference being squared in squaring circuit 94. The difference between Y and Y, is determined at summer 96. the square of the difference being taken at multiplier 98. The square root of the sum ofthe squares produced by multipliers 94 and 98 is determined by square rooting circuit 100 and summer 102. Hence. the output signal from square root circuit I is a measure of the distance between the points X Y and X,. Y,.

In accordance with the foregoing formula for the center of force the length of the side between X Y and X,. Y, is multiplied by the J. co-ordinate at multiplier I04 and the y co-ordinate at multiplier 106. After this multiplication occurs these signals are gated to accumulator cells I08, I10, and I12 by gates 114, I16, and 118 respectively. Thus. the accumulators 108 through 112 successively accumulate the qualities specified in the foregoing formulas. the sine pulse being applied to gates 114 through 118 each time a new pair of co-ordinates defining a given side are applied to the terminals 80-86. These co-ordinates would be typically provided from two scanners which scan the cells I of FIG. I where one scanner would be one co-ordinate point behind the other. The co-ordinate points are successively applied to the circuitry of FIG. 8 until all successive pairs have been processed. It should be noted that a curve on the cavity contour can be readily approximated by a succession of small straight line segments as is well known and thus, the end points of these small straight line segments would also be processed by the circuitry of FIG. 8 as the other end points described above.

As the calculations are being summed in accumulators 108 and I12, the output of accumulator 108 is being continuously divided by the output of accumulator 112 at divider 120 while the output of accumulator 110 is being divided by the output of accumulator H2 at divider 122. After all pairs of end points have been processed, the outputs of dividers 120 and 122 may be gated to provide the coordinates X and Y, which correspond to the center of force of the object and which are stored in cell 3 of FIG. 1 for use in various processing units such as that described hereinbefore with re spect to FIG. 6.

Reference should now be made to FIG. 10 which shows illustrative circuitry for determining whether axes of symmetry exist for a given die configuration. Reference should also be made to FIG. ll which illustrates a typical symmetrical body for which the angle of an axis of symmetry is to be determined. The coordinates X,-, Y of the center of force are determined by the circuitry of FIG. 8 as described hereinbefore and the general approach is to successively rotate an axis incrementally about the center of force through a total angle of 180 (This is done merely by incrementing the magnitude of a signal representing the axis angle.) whereby at each angular increment, a test is made to determine whether or not symmetry exists. When the axis has been stepped to the angle or shown in FIG. 11, this angle will be applied to the circuitry of FIG. 10 as indicated thereat. The blocks 122 and 124 are exactly the same as the blocks 50 and 72 of FIG. 6 while the blocks 126 and I28 are also exactly the same. As stated before, blocks 122 and 124 determine the rotated vertical co-ordinates corresponding to the vertical coordinates of a point in an original co-ordinate system. Blocks 126 and 128 determine the horizontal coordinates in the rotated system. The formula for implementing this is as follows: .r, X,,X,-)cosa (Y Y, )sina where X Y and X, ,Y are defined as hereinbefore for y.,,,,,,,,.,,,.

The corresponding circuitry is shown in block 128 of FIG. I0. Referring to FIG. II, it can be seen that in the rotated system the points X,. Y, and X Y have the same .r co-ordinate and equal but opposite coordinates. It is this fact which is utilized to establish whether an axis of symmetry occurs at the angle 01. Hence, assuming the angle a has been stepped to the value indicated in FIG. II, the output signals from blocks 126 and 128 will be equal since. as stated above, the .r co-ordinates of the points X,, Y, and X Y, are equal and since X Y, are applied to block 126 while X,, Y, are applied to block I28. The outputs from blocks I22 and I24 will be equal and opposite. The output from block 124 is applied to a unity gain inverting amplifier 130. Thus, all of the signals applied to differential amplifiers 132 will be equal and thus no output will occur from either of these amplifiers. Further, no output will occur from OR circuit 136 and thus the lack of an output signal therefrom indicates that the first test for symmetry at angle a has been passed. The co-ordinates stored in cells 1 of the contour are scanned by two scanners. Since the symmetry test was passed for the first pair of points, the first scanner is stepped forward to apply the co-ordinates X Y to the blocks I22 and 126 while the second scanner is stepped back to apply the co-ordinates of the point X,,, Y, to the blocks 124 and 128. The test described above is again performed and as indicated at FIG. I0 it will again be passed thereby indicating that the next pair of significant points should be processed whereby the above procedure is repeated. Since the number of pairs of significant points is known, the number of times the aforementioned two scanners are respectively incremented and decremented is also known. After all symmetry tests have been passed, the determination that the axis oriented at the angle a is indeed an axis of symmetry is made final and this angle is stored in one of the cells 2 of FIG. I.

Numerous modifications of the invention will become apparent to one of ordinary skill in the art upon reading the foregoing disclosure. During such a reading it will be evident that this invention provides a unique method and apparatus for automatically splitting a die cavity for accomplishing the objects and advantages hereinstated.

What is claimed is:

1. Apparatus for automatically splitting a die cavity, said apparatus comprising means for storing contour characteristic signals representative of significant characteristics of the contour of the die cavity; and

means responsive to said storing means for processing the stored signals to determine the split lines for dividing said cavity into segments which can be expeditiously machined.

2. Apparatus as in claim 1 where said processing means includes means for assigning a first weight to a first of said contour characteristic signals and a second weight to a second of said contour characteristic signals and further means responsive to the weighted first and second contour characteristic signals for determining which group of said latter signals corresponds to the best suitable split lines.

Apparatus as in claim 2 where said further means includes means for summing each group oi said first and second contour characteristic signals and means for selecting the group having the highest sum as that group which corresponds to the best suitable split lines 4. Apparatus as in claim 2 where said group comprises a pair which corresponds to two split lines.

5. Apparatus as in claim 1 wherein said contour has at least one axis of symmetry and where said storing means includes means for storing angle signals representative of the angle of each axis of symmetry of said contour. means for storing cumulative parallel side sig nals representative of the total length of all sides of said contour parallel to each axis of symmetry. and where said processing means includes means responsive to said angle signals and said cumulative parallel side signals for determining which axis of symmetry is best suited for said split lines.

6. Apparatus as in claim 5 where said processing means includes means for assigning a first weight to said angle signals and a second weight to said cumulative parallel side signals. and further means responsive to the weighted angle and cumulative parallel side sig nals for determining which axis of symmetry is best suited for said split lines.

7. Apparatus as in claim 6 where said further means includes means for summing each pair of said angle signals and cumulative parallel side signals and means for selecting the pair having the highest sum as that axis of symmetry best suited for said split lines.

8. Apparatus as in claim 5 where said storing means includes means for storing end point signals representative of the co-ordinates of the end points of all straight line segments in said contour and where said processing means includes means responsive to said end point signals and said angle signals for determining said cumulative parallel side signal for each angle signal.

9. Apparatus as in claim 8 where said processing means includes means responsive to said end point signals for determining the angle of each said line segment; means for comparing the angle of each line segment with said angle signal corresponding to the axis of symmetry; means for determining the length of each line segment; and means for accumulating the lengths of all line segments parallel to said axis of symmetry to thereby determine said cumulative parallel side signal for each axis of symmetry.

10. Apparatus as in claim 1 where said contour is non-symmetrical and where said storing means includes means for storing angle signals representative of the angles between each pair of possible split lines and means for storing mutual length signals respectively corresponding to the distance between said possible split lines where they intersect said contour and where said processing means includes means responsive to said angle signals and said mutual distance signals for determining which pair of angle signals and mutual distance signals corresponds to the best suitable split lines.

11. Apparatus as in claim 10 where said processing means includes means for assigning a first weight to said angle signals and a second weight to said mutual distance signals and further means responsive to the weighted angle and mutual distance signals for determining which pair of angle and mutual distance signals corresponds to the best suitable split lines.

12. Apparatus as in claim ll where said further means includes means for summing each pair of said 12 angle signals and mutual distance signals and means for selecting the pair having the highest sum as that which corresponds to the best suitable split lines.

l3. Apparatus as in claim 1 where said contour has at least one axis of symmetry and where said storing means includes means for storing orientation signals representative of the orientation of each axis ofsymmetry of said contour and curved portion signals representative of the location of curved portion of said contour and where said processing means includes means responsive to said orientation signal and said curved portion signals for determining whether each said axis of symmetry passes through any of said curved portions.

14. Apparatus as in claim 1 where said contour has at least one axis of symmetry and where said storing means includes means for storing angle signals representative of the angle of each axis of symmetry of said contour and means for storing concavity signals indicating whether each curved portion of said contour is concave and where said processing means includes means responsive to said angle signals and said concavity signals for determining whether any concave portions of said contour are intersected by an axis of symmetry whereby any axis which does intersect a said concave portion is not suitable for said split lines.

15. Apparatus as in claim 14 where said storing means includes means for storing center of force signals representative of the co-ordinates of the center of force of said contour and curved portion signals defining the end points of each curved portion of said contour; and where said processing means includes first means responsive to said curved portion signals, said center of force signals, and said angle signals for determining whether said axis of symmetry passes through said curved portions and second means responsive to the output signal from said first means and said concav ity signal for determining whether any concave por tions of said contour are intersected by an axis of symmetry.

16. Apparatus as in claim 15 including means for calculating said center of force signals.

17. Apparatus as in claim 14 including means for calculating said angle signals.

18. A method for automatically splitting a die cavity. said method comprising storing electrical, contour characteristic signals representative of significant characteristics of the contour of the die cavity; and

processing, in response to said storing step, the stored signals to determine the split lines for dividing said cavity into segments which can be expeditiously machined.

19. A method as in claim 18 where said processing step includes assigning a first weight to a first of said contour characteristic signals and a second weight to a second of said contour characteristic signals and further determining, in response to the weighted first and second contour characteristic signals, which group of said latter signals corresponds to the best suitable split lines.

20. A method as in claim 19 where said further processing step includes summing each group of said first and second contour characteristic signals and selecting the group having the highest sum as that group which corresponds to the best suitable split lines.

21. A method as in claim 19 where said group comprises a pair which corresponds to two split lines.

22. A method as in claim 18 where said contour has at least one axis of symmetry and where said storing step includes storing angle signals representative of the angle of each axis of symmetry of said contour and storing cumulative parallel side signals representative of the total length of all sides of said contour parallel to each axis of symmetry; and where said processing step includes determining, in response to said angle signals and said cumulative parallel sidc signals, which axis of symmetry is best suited for said split lines.

23. A method as in claim 22 where said processing step includes assigning a first weight to said angle signals and a second weight to said cumulative parallel side signals, and further determining, in response to the weighted angle and cumulative parallel side signals, which axis of symmetry is best suited for said split lines.

24. A method as in claim 23 where said further determining step includes summing each pair of said angle signals and cumulative parallel side signals and selecting the pair having the highest sum as that axis of symmetry best suited for said split lines.

25. A method as in claim 24 where said storing step includes storing end point signals representative of the co-ordinates of the end points of all straight line segments in said contour and where said processing step includes determining, in response to said end point signals and said angle signals, said cumulative parallel side signal for each angle signal.

26. A method as in claim 25 where said processing step includes determining, in response to said end point signals, the angle of each said line segment; comparing the angle of each line segment with said angle signal corresponding to the axis of symmetry; determining the length of each line segment; and accumulating the lengths of all line segments parallel to said axis of symmetry to thereby determine said cumulative parallel side signal for each axis of symmetry.

27. A method as in claim 18 where said contour is non-symmetrical and where said storing step includes storing angle signals representative of the angles between each pair of possible split lines and storing mutual length signals respectively corresponding to the distance between said possible split lines where they intersect said contour and where said processing step includes determining, in response to said angle signals and said mutual distance signals, which pair of angle signals and mutual distance signals corresponds to the best suitable split lines.

28. A method as in claim 27 where said processing step includes assigning a first weight to said angle signals and a second weight to said mutual distance signals and further determining, in response to the weighted angle and mutual distance signals, which pair of angle and mutual distance signals corresponds to the best suitable split lines.

29. A method as in claim 28 where said further determining step includes summing each pair of said angle signals and mutual distance signals and selecting the pair having the highest sum as that which corresponds to the best suitable split lines.

30. A method as in claim 18 where said contour has at least one axis of symmetry and where said storing step includes storing orientation signals representative of the orientation of each axis of symmetry of said contour and curved portion signals representative of the location of curved portions of said contour and where said processing step includes determining, in response to said orientation signals and said curved portion signals, whether each said axis of symmetry passes through any of said curved portions.

31. A method as in claim 18 where said contour has at least one axis of symmetry and where said storing step includes storing angle signals representative of the angle ofeach axis of symmetry of said contour and storing concavity signals indicating whether each curved portion of said contour is concave and where said processing step includes determining, in response to said angle signals and said concavity signals whether any concave portions of said contour are intersected by an axis of symmetry whereby any axis which does intersect a said concave portion is not suitable for said split lines.

32. A method as in claim 31 where said storing step includes storing center of force signals representative of the co-ordinates of the center of force of said contour and curved portion signals defining the end points of each curved portion of said contour; and where said processing step includes first determining, in response to said curved portion signals, said center of force signals, and said angle signals, whether said axis of symmetry passes through said curved portions and second determining, in response to the output signal from said first determining step and said concavity signal, whether any concave portions of said contour are intersected by an axis of symmetry.

33. A method as in claim 32 including calculating said center of force signals.

34. A method as in claim 31 including calculating said angle signals. 

1. Apparatus for automatically splitting a die cavity, said apparatus comprising means for storing contour characteristic signals representative of significant characteristics of the contour of the die cavity; and means responsive to said storing means for processing the stored signals to determine the split lines for dividing said cavity into segments which can be expeditiously machined.
 2. Apparatus as in claim 1 where said processing means includes means for asSigning a first weight to a first of said contour characteristic signals and a second weight to a second of said contour characteristic signals and further means responsive to the weighted first and second contour characteristic signals for determining which group of said latter signals corresponds to the best suitable split lines.
 3. Apparatus as in claim 2 where said further means includes means for summing each group of said first and second contour characteristic signals and means for selecting the group having the highest sum as that group which corresponds to the best suitable split lines.
 4. Apparatus as in claim 2 where said group comprises a pair which corresponds to two split lines.
 5. Apparatus as in claim 1 wherein said contour has at least one axis of symmetry and where said storing means includes means for storing angle signals representative of the angle of each axis of symmetry of said contour, means for storing cumulative parallel side signals representative of the total length of all sides of said contour parallel to each axis of symmetry, and where said processing means includes means responsive to said angle signals and said cumulative parallel side signals for determining which axis of symmetry is best suited for said split lines.
 6. Apparatus as in claim 5 where said processing means includes means for assigning a first weight to said angle signals and a second weight to said cumulative parallel side signals, and further means responsive to the weighted angle and cumulative parallel side signals for determining which axis of symmetry is best suited for said split lines.
 7. Apparatus as in claim 6 where said further means includes means for summing each pair of said angle signals and cumulative parallel side signals and means for selecting the pair having the highest sum as that axis of symmetry best suited for said split lines.
 8. Apparatus as in claim 5 where said storing means includes means for storing end point signals representative of the co-ordinates of the end points of all straight line segments in said contour and where said processing means includes means responsive to said end point signals and said angle signals for determining said cumulative parallel side signal for each angle signal.
 9. Apparatus as in claim 8 where said processing means includes means responsive to said end point signals for determining the angle of each said line segment; means for comparing the angle of each line segment with said angle signal corresponding to the axis of symmetry; means for determining the length of each line segment; and means for accumulating the lengths of all line segments parallel to said axis of symmetry to thereby determine said cumulative parallel side signal for each axis of symmetry.
 10. Apparatus as in claim 1 where said contour is non-symmetrical and where said storing means includes means for storing angle signals representative of the angles between each pair of possible split lines and means for storing mutual length signals respectively corresponding to the distance between said possible split lines where they intersect said contour and where said processing means includes means responsive to said angle signals and said mutual distance signals for determining which pair of angle signals and mutual distance signals corresponds to the best suitable split lines.
 11. Apparatus as in claim 10 where said processing means includes means for assigning a first weight to said angle signals and a second weight to said mutual distance signals and further means responsive to the weighted angle and mutual distance signals for determining which pair of angle and mutual distance signals corresponds to the best suitable split lines.
 12. Apparatus as in claim 11 where said further means includes means for summing each pair of said angle signals and mutual distance signals and means for selecting the pair having the highest sum as that which corresponds to the best suitable split lines.
 13. Apparatus as in claim 1 where Said contour has at least one axis of symmetry and where said storing means includes means for storing orientation signals representative of the orientation of each axis of symmetry of said contour and curved portion signals representative of the location of curved portion of said contour and where said processing means includes means responsive to said orientation signal and said curved portion signals for determining whether each said axis of symmetry passes through any of said curved portions.
 14. Apparatus as in claim 1 where said contour has at least one axis of symmetry and where said storing means includes means for storing angle signals representative of the angle of each axis of symmetry of said contour and means for storing concavity signals indicating whether each curved portion of said contour is concave and where said processing means includes means responsive to said angle signals and said concavity signals for determining whether any concave portions of said contour are intersected by an axis of symmetry whereby any axis which does intersect a said concave portion is not suitable for said split lines.
 15. Apparatus as in claim 14 where said storing means includes means for storing center of force signals representative of the co-ordinates of the center of force of said contour and curved portion signals defining the end points of each curved portion of said contour; and where said processing means includes first means responsive to said curved portion signals, said center of force signals, and said angle signals for determining whether said axis of symmetry passes through said curved portions and second means responsive to the output signal from said first means and said concavity signal for determining whether any concave portions of said contour are intersected by an axis of symmetry.
 16. Apparatus as in claim 15 including means for calculating said center of force signals.
 17. Apparatus as in claim 14 including means for calculating said angle signals.
 18. A method for automatically splitting a die cavity, said method comprising storing electrical, contour characteristic signals representative of significant characteristics of the contour of the die cavity; and processing, in response to said storing step, the stored signals to determine the split lines for dividing said cavity into segments which can be expeditiously machined.
 19. A method as in claim 18 where said processing step includes assigning a first weight to a first of said contour characteristic signals and a second weight to a second of said contour characteristic signals and further determining, in response to the weighted first and second contour characteristic signals, which group of said latter signals corresponds to the best suitable split lines.
 20. A method as in claim 19 where said further processing step includes summing each group of said first and second contour characteristic signals and selecting the group having the highest sum as that group which corresponds to the best suitable split lines.
 21. A method as in claim 19 where said group comprises a pair which corresponds to two split lines.
 22. A method as in claim 18 where said contour has at least one axis of symmetry and where said storing step includes storing angle signals representative of the angle of each axis of symmetry of said contour and storing cumulative parallel side signals representative of the total length of all sides of said contour parallel to each axis of symmetry; and where said processing step includes determining, in response to said angle signals and said cumulative parallel side signals, which axis of symmetry is best suited for said split lines.
 23. A method as in claim 22 where said processing step includes assigning a first weight to said angle signals and a second weight to said cumulative parallel side signals, and further determining, in response to the weighted angle and cumulative parallel side signals, which axis of symmetry is best suited for said split lines.
 24. A method as in claim 23 where said further determining step includes summing each pair of said angle signals and cumulative parallel side signals and selecting the pair having the highest sum as that axis of symmetry best suited for said split lines.
 25. A method as in claim 24 where said storing step includes storing end point signals representative of the co-ordinates of the end points of all straight line segments in said contour and where said processing step includes determining, in response to said end point signals and said angle signals, said cumulative parallel side signal for each angle signal.
 26. A method as in claim 25 where said processing step includes determining, in response to said end point signals, the angle of each said line segment; comparing the angle of each line segment with said angle signal corresponding to the axis of symmetry; determining the length of each line segment; and accumulating the lengths of all line segments parallel to said axis of symmetry to thereby determine said cumulative parallel side signal for each axis of symmetry.
 27. A method as in claim 18 where said contour is non-symmetrical and where said storing step includes storing angle signals representative of the angles between each pair of possible split lines and storing mutual length signals respectively corresponding to the distance between said possible split lines where they intersect said contour and where said processing step includes determining, in response to said angle signals and said mutual distance signals, which pair of angle signals and mutual distance signals corresponds to the best suitable split lines.
 28. A method as in claim 27 where said processing step includes assigning a first weight to said angle signals and a second weight to said mutual distance signals and further determining, in response to the weighted angle and mutual distance signals, which pair of angle and mutual distance signals corresponds to the best suitable split lines.
 29. A method as in claim 28 where said further determining step includes summing each pair of said angle signals and mutual distance signals and selecting the pair having the highest sum as that which corresponds to the best suitable split lines.
 30. A method as in claim 18 where said contour has at least one axis of symmetry and where said storing step includes storing orientation signals representative of the orientation of each axis of symmetry of said contour and curved portion signals representative of the location of curved portions of said contour and where said processing step includes determining, in response to said orientation signals and said curved portion signals, whether each said axis of symmetry passes through any of said curved portions.
 31. A method as in claim 18 where said contour has at least one axis of symmetry and where said storing step includes storing angle signals representative of the angle of each axis of symmetry of said contour and storing concavity signals indicating whether each curved portion of said contour is concave and where said processing step includes determining, in response to said angle signals and said concavity signals whether any concave portions of said contour are intersected by an axis of symmetry whereby any axis which does intersect a said concave portion is not suitable for said split lines.
 32. A method as in claim 31 where said storing step includes storing center of force signals representative of the co-ordinates of the center of force of said contour and curved portion signals defining the end points of each curved portion of said contour; and where said processing step includes first determining, in response to said curved portion signals, said center of force signals, and said angle signals, whether said axis of symmetry passes through said curved portions and second determining, in response to the output signal from said first determining step and said concavity signal, whether any concave portions of said contour are intersected by an axis of symmetry.
 33. A method as in claim 32 including calculating said center of force signals.
 34. A method as in claim 31 including calculating said angle signals. 